Computers and Electronics in Agriculture 99 (2013) 146–152

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Computers and Electronics in Agriculture

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Three dimensional finite element model of soil compaction caused byagricultural tire traffic

0168-1699/$ - see front matter � 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.compag.2013.08.026

⇑ Corresponding author at: Departamento de Ingeniería Agrícola, Facultad deCiencias Agropecuarias, Universidad Central ‘‘Marta Abreu’’ de las Villas (UCLV),Carretera a Camajuaní km 5.5, Santa Clara 54830, Villa Clara, Cuba. Tel.: +5342281692; fax: +53 42281608.

E-mail address: omar@uclv.edu.cu (O. González Cueto).1 Tel.: +53 42281692.

Omar González Cueto a,⇑,1, Ciro E. Iglesias Coronel b, Carlos A. Recarey Morfa c, Guillermo Urriolagoitia Sosa d,Luís H. Hernández Gómez d, Guillermo Urriolagoitia Calderón d, Miguel Herrera Suárez a,1

a Departamento de Ingeniería Agrícola, Facultad de Ciencias Agropecuarias, Universidad Central ‘‘Marta Abreu’’ de las Villas (UCLV), Carretera a Camajuaní km 5.5, Santa Clara54830, Villa Clara, Cubab Centro de Mecanización Agropecuaria, Facultad de Ciencias Técnicas, Universidad Agraria de la Habana (UNAH), San José de las Lajas, Mayabeque, Cubac Centro de Investigación en Métodos Computacionales y Numéricos en la Ingeniería, Facultad de Construcciones, Universidad Central ‘‘Marta Abreu’’ de las Villas (UCLV), Carretera aCamajuaní km 5.5, Santa Clara 54830, Villa Clara, Cubad Sección de Estudios de Postgrado e Investigación, Escuela Superior de Ingeniería Mecánica y Eléctrica, Unidad Profesional Adolfo López Mateos ‘‘Zacatenco’’, Instituto PolitécnicoNacional, Edificio 5, 2do. Piso, Col. Lindavista, CP 07738 México, D.F., Mexico

a r t i c l e i n f o

Article history:Received 22 March 2013Received in revised form 30 August 2013Accepted 31 August 2013

Keywords:FEMSoil compaction simulationWheelSoil stresses

a b s t r a c t

Most of the finite element models of soil compaction do not represent the tire, only the effect of a uniformground stress is distributed on a soil area with a preset form. It constitutes an oversimplification of theproblem and it would yield erroneous contact conditions, because the tire–soil contact stress distributionis the result of simultaneous tire and soil deformation. This research was carried out with the objective ofdeveloping a model, valid for soil compaction simulation caused by agricultural tire traffic that allowsresearch factors that cause soil compaction of a Rhodic Ferralsol soil. The tire was developed as a uniquesolid layer, which represents its mean properties with a linear elastic constitutive model. Predictions ofdeflection and tire contact area in rigid surface were compared with experimental results and the tiremodel was validated. A three dimensional model of the soil was created and the soil properties were rep-resented with an Extended Drucker Prager material model. ABAQUS/STANDARD 6.8-1 code was used todevelop the tire–soil interaction model. A tire traffic experiment was carried out at a soil bin to two soilwater conditions, tire inflation pressures and tire load. Triaxial and direct shear tests were used to obtainsoil properties and constitutive parameters. Predictions were compared with experimental results to ver-ify the validity of the model in each soil water content. Simulated and observed stresses after wheel traf-fic under different inflation pressures and tire loads agree well. The model predicts the effect of inflationpressures, ground pressure and tire load on the stresses on the contact and the soil profile, it can be usedin both teaching and research. The model was used to predict the depth at which soil compaction wasproduced for each combination of tire inflation pressure and tire load, and the relationship betweenthe tire inflation pressure, contact stress and tire load with soil compaction. The model showed that mag-nitudes of vertical stresses transmitted to soil are independent to water content and that more soil com-paction in wet soils depends on the less yield stresses in those conditions. Besides, the good agreement ofthe model with experimental results demonstrates the validity of using the Extended Drucker Pragermodel to represent the mechanical response of the Rhodic Ferralsol soil.

� 2013 Elsevier B.V. All rights reserved.

1. Introduction

Bai et al. (2008) define land degradation as a long-term loss ofecosystem function and productivity caused by disturbances from

which the land cannot recover unaided. This phenomenon hasgrown from 15% of the world territory in 1991 to 23.54% in 2003,and inside this, 19% is referred to croplands (Bai et al., 2008). TheWorld map of the status of human-induced soil degradation refersto the soil compaction among the most important factors thatcause land degradation (Oldeman et al., 1991).

Soil compaction has become a major environmental problemand diverse modeling techniques have been used to predict the soilresponse to the traffic of agricultural vehicles. Soil compactionmodels permit the prediction of the stresses distribution in the soilprofile and of the change in the bulk density or other variables due

Nomenclature

E Young’s modulus of elasticity (kPa)G shear modulus (kPa)Gs specific gravity (g cm�3)K flow stress coefficientL load tire (kN)LL liquid limit (%)OM organic matter (%)p mean normal stress (kPa)PI plasticity indexPi tire inflation pressure (kPa)PL plastic limit (%)t deviatory stress (kPa)w water content (g 100 g�1)wopt optimum water content (g 100 g�1)Pi ex experimental tire inflation pressure (kPa)

Pi si simulation tire inflation pressure (kPa)

Greek lettersb friction angle of the material (�)l friction coefficientrf yield stress (kPa)w dilatancy angle (�)m Poisson’s coefficientrz vertical stress (kPa)c concentration factora half aperture angle between the point at depth z and the

contact area’s edge (�)q bulk density (Mg m�3)

O. González Cueto et al. / Computers and Electronics in Agriculture 99 (2013) 146–152 147

to the machinery traffic. The modeling allows to make recommen-dations to the farmers and advisors with regard to the technologiesand agricultural equipment to use in order to reduce the risk of soilcompaction. Besides, the depth until which the compaction takesplace or the depth of the hardpan layer can be established. It alsoconstitutes an important source of information for tire and equip-ment designers, in order to predict the behavior of their productsover a soil.

Soil compaction models have been based on three main meth-ods: a pseudo-analytic procedure, a numerical calculus based onthe finite element method (FEM) (Défosssez and Richard, 2002)and empirical methods. These last ones are based on parametersthat combine characteristics of the loads, the running gears andthe soil properties. The traffic effect is predicted by empirical equa-tions from the change of the initial conditions of the soil bulk den-sity, cone index, hydraulic conductivity, air and waterpermeability, porosity and other traffic variables (Canillas andSalokhe, 2002).

Pseudo-analytical model establishes a solution for the propaga-tion of stresses caused by a punctual load or load with a circulardistribution. The soil is assumed as a semi-infinite dominium,which is homogeneous, isotropic and ideal elastic (Boussinesq,1885). This approach, with its later modifications (Fröhlich, 1934;Söhne, 1953), was used as the theoretical basis of many models,which have been recently developed (Arvidsson et al., 2001; Kelleret al., 2007; Schjønning et al., 2008; Van den Akker, 2004). Défossezand Richard (2002) revised, with field tests, the models proposedby O’Sullivan et al. (1999) and Arvidsson et al. (2001). They foundthat this pseudo-analytical approach was adequate for simulatinghomogeneous soils, which are 0.5–1 m of depth. In subsoil layers,because the material is more homogeneous and stiffer the defor-mations are smaller. More accurate predictions are obtained thanin top layer, since soil deformation is not only elastic, but in agreater extent, is plastic (Söhne, 1958).

Keller et al. (2007) developed an analytical soil compactionmodel (SoilFlex). It includes all the useful aspects from these exist-ing models in a new, two-dimensional, model. It considers normaland shear stresses on the surface. The stress propagation throughsoil is calculated analytically and the soil deformation is evaluatedas a function of the stresses. This model solves some limitations ofthe previous ones, such as the estimation of the upper boundarycondition between tire and soil. It is possible to consider anyuser-defined contact area and stress distribution. In contrast tomany soil compaction models, the input data can consider dualand triple wheels. Although, the upper boundary conditions

between tire and soil are improved in this model, the analyticaland pseudo-analytical approach preset the shape and dimensionsof contact area and the stress distribution in the tire–soil interface.

The finite element method (FEM) has a better potential toobtain results that are more precise because a smaller number ofsuppositions and simplifications are introduced. The geometryand dimensions of the tire contact area is the result of the tire–soildeformation. Therefore, a better precision is achieved in the predic-tions of contact stresses, stresses propagation and plastic volumet-ric strains in the soil (Liu and Wong, 1996).

The finite element models of tire–soil interaction can be classi-fied into two groups. The first one includes the models related withsoil compaction and the effects of agricultural equipment over thesoil (Biris et al., 2009; Cui et al., 2007; Gysi et al., 2000; Kirby et al.,1997; Poodt et al., 2003). The main limitation of most of thesemodels is that tire is not represented. Only the effect of a uniformground pressure is simulated on a soil area with a preset form. Itconstitutes an oversimplification of the problem and it would yielderroneous contact conditions, because the tire–soil contact stressdistribution is the result of simultaneous tire and soil deformation(González, 2011). It depends on the stiffness, lug pattern and tiretread, soil strength and dynamic forces acting over tire (Keller,2004).

The second group includes the finite element models used inthe design of tires, trafficability, vehicle dynamics and develop-ment of off road vehicles (Gruber et al., 2008; Hall et al., 2004;Shoop, 2001; Tönük and Ünlüsoy, 2001; Yan, 2001). Most of thesemodels make a detailed tire representation that includes all ele-ments of its structure (steel bead, belts, plies and rubber, amongothers), but these models do not included the effects of the tiretraffic on the soil. They demand a very high computational capacityand expensive specialized tests to obtain the properties of thematerials involved.

The solution of tire–soil interaction problems with FEM can bedivided into three parts: the tire modeling, the soil modeling, andthe combined tire–soil interaction model (Shoop, 2001). If a threedimensional model of the tire is developed as a unique solid layer,which represents its mean properties with a linear elastic constitu-tive model, and a three dimensional model of the soil is created, itis possible to simulate the interaction between both models. In thisway, the contact area and the contact stress distribution will be theresults of tire and soil simultaneous deformation. This solves thelimitations of soil compactions models and saves computingresources. From these elements this research was carried out withthe objective of developing a model, valid for soil compaction

Run time. Contact area12014000

10012000

) m2 )

148 O. González Cueto et al. / Computers and Electronics in Agriculture 99 (2013) 146–152

simulation caused by agricultural tire traffic, by means of the FEM,that allows research factors that cause soil compaction of a RhodicFerralsol soil.

8010000

606000

8000

40Run

tim

e (s

202000

4000

Con

tact

are

a (c

002.5 5 6 10 15 20

Elements dimensions (mm)

Fig. 2. Tire contact area and run time on function of the mesh density.

2. Soil compaction model

In order to obtain a soil compaction model a three dimensionaltire model was developed initially. Later, it was validated withexperimental results. For this purpose, the tire deflection and tirecontact area on a rigid surface were evaluated. In a next step, a threedimensional soil model was generated like a soil block with materialproperties of a Rhodic Ferralsol soil. Then simulation of the soilcompaction was obtained from the interaction of the tire and soilmodels. The last step was the validation of the soil compaction mod-el with an experiment carried out on a soil bin. For the numericalanalysis ABAQUS/STANDARD 6.8-1 code was used. It is a general-purpose finite element program and is commonly used to simulatethe tire–soil interaction (Fervers, 2004; Ghoreishy, 2006; González,2011; Hambleton and Drescher, 2009; Shoop, 2001).

2.1. Development of the finite element tire model

The process of tire compression over a rigid surface was repre-sented with the goal of determining the deflection and contact areaunder different inflation pressure (Pi) and applied load (L). Thephysical characteristics were simplified in the tire modeling withthe objective of improving the computational efficiency. Moreover,it is impossible to include all the tires details in a numerical modeldue to the diversity of tires available. Therefore, some simplifica-tions must be introduced during the development of the tire modelbased on the objectives of analysis (Hu and Abeels, 1994). Thesesimplifications can include the tire idealization like a single layerand smooth tread, which represents the composite behavior ofeach parts components. For the problem at hand, the tire was mod-eled as a three-dimensional solid layer with a smooth tread. It rep-resents the complexity of the structural components of the tire,which consists on layers of belts, plies, and a steel bead imbeddedin rubber. The selected pneumatic tire was a 3.5 � 10 bias ply. It isused as a tractive wheel at the tubers planter. Although this tirehas small dimensions, the range of its inflation pressures and staticground pressures is similar to those of many agricultural front andrear tractor tire. Fig. 1 shows the geometrical model and the origi-nal tire.

It has to be kept in mind that it is difficult and expensive toobtain the real mechanical properties of a tire. Therefore, linearelastic properties have been used to represent the tire constitutivemodel. The Poisson’s coefficient (m) was 0.48, assuming that thevolume change during tire deformation is negligible (Hu and Abe-els, 1994; Nakashima and Wong, 1993). The Young’s modulus (E)was obtained by an inverse analysis technique. E was calibrated

Fig. 1. Geometrical model and the original tire.

by iteratively changing its value, until the simulated deflectionand contact area matched with the observed data. The stiffnessof the tire changes with the inflation pressure and the applied load,for that reason E was obtained for each load condition and inflationpressure evaluated.

Contact is a physical interaction between two surfaces that mayinteract with each other as a contact pair. The problem presentedhere is the contact between a deformable body and a rigid surface.It must be chosen which of the surfaces will be the slave and whichone will be the master (Abaqus, 2008). The rigid surface was se-lected as master and the tire as slave. The interaction properties in-cluded those originated by normal and tangential interaction overthe tire–soil interface. The tangential contact property was estab-lished with the friction formulation of penalty and the frictioncoefficient used was 0.5 (Hambleton and Drescher, 2009).

The tire model was developed, establishing a kinematic cou-pling constrain between a reference node in the center of the tireand the tire bead, simulating a rigid rim that controls the displace-ment of the whole tire. The loading conditions were determined intwo steps. In the first one, a uniform pressure was applied over theinterior surface of the tire. In the second one, a concentrated forcewas applied on the reference node.

For the tire discretization, hybrid elements are frequently used(Ghoreishy, 2006; Gruber et al., 2008; Grujicic et al., 2009; Hu andAbeels, 1994; Suripa and Chaikittiratana, 2008). Hu and Abeels(1994) mention that hybrid elements are especially appropriatedto model incompressible material like rubber. Therefore, the tirewas modeled with linear bricks of eight nodes, hybrid elements.

The mesh density was selected from a mesh convergence study.Analyses with a series of finer meshes were run until the conver-gence between the predicted contact area and contact area mea-sured experimentally was within an error range of 5%. At thepoint where the analysis with a series of finer meshes reaches suf-ficiently small changes in the numerical results, it is assumed thatthe finite element solution converges to the exact solution of themechanical model with enough accuracy for the physical problem(Hu and Abeels, 1994). Fig. 2 shows constant values for contactarea from elements dimensions less than 6 mm. For elementssmaller than 5 mm, the run time was excessively high, demandingexcessive computational costs. From these results, it was definedthat the elements of 6 mm were appropriate for tire mesh.

2.2. Validation of the finite element tire model

In order to validate the tire model, the deflection and tire con-tact area were experimentally determined for several load-infla-tion pressure combinations. Four load levels (0.7, 1.3, 1.7 and2.3 kN) and three inflation pressures (100, 160 and 325 kPa) wereselected respecting peak load of 2.4 kN and peak inflation pressureof 325 kPa recommended by tire manufacturer. Each combinationof tire loads was obtained by means of steel ballasts, which weresituated on the frame over the tire. The wheel was placed, in such

Fig. 3. Determination of tire contact area.

30

Pi ex = 325 kPa Pi ex = 160 kPa Pi ex = 100 kPaPi si = 325 kPa Pi si = 160 kPa Pi si = 100 kPa

5

1015

20

25

Def

lect

ion

(mm

)

00 0.5 1 1.5 2 2.5

Tire load (kN)

Fig. 4. Experimental results of deflection versus simulation.

Pi ex = 325 kPa Pi ex = 160 kPa Pi ex = 100 kPaPi si = 325 kPa Pi si = 160 kPa Pi si = 100 kPa

100

80

60

40

20

Con

act a

rea,

(cm

2 )

00 0.5 1 1.5 2 2.5

Tire load (kN)

Fig. 5. Experimental results of contact area versus simulation.

O. González Cueto et al. / Computers and Electronics in Agriculture 99 (2013) 146–152 149

Table 1Constitutive parameters of Drucker Prager Extended material model.

w (g 100 g�1) E (kPa) m rf (kPa) b� K W�

25 16000 0.34 106 23 1 2330 1200 0.24 55 9 1 0

Where, w – water content; E – module of elasticity; m – Poisson’s coefficient; rf –yield stress; b – friction angle of the material; K – flow stress coefficient; W –dilatancy angle.

way that it had free motion along the vertical axis. The deflectionwas determined as the difference between static unloaded tirediameter and static loaded tire diameter. For the measurement oftire contact area on a rigid surface (Fig. 3), a white paper wasplaced at the center of a steel plate and a blue carbon paper wassituated on the paper. The plate with the carbon paper was placedbelow the tire. The imprint of the tire on the white paper was ob-tained by applying the entire weight of the tire over the blue car-bon paper for 5 or 6 s and later the outline of the contact areaimprint was traced (Kumar and Dewangan, 2004; Upadhyaya andWulfsohn, 1990). Three replications were done. The paper withthe imprint of contact area was scanned and the contact areawas determined by digital image processing (Gysi et al., 2000).

2.2.1. Results of the validation of the finite element tire modelFigs. 4 and 5 show that there is a close relationship between the

experimental results (deflection and contact area of the tire) withthe models predictions. To determine the relationship betweenthe experimental and simulation results, a linear regression analy-sis was carried out. The probability values were less than 0.05 andcorrelation and R2 coefficients for contact area were 0.9955 and99.11%, respectively; and 75.93% and 0.8716 for tire deflection.These results demonstrated in both cases, that the relationshipsare statistically significant. The good agreement between the mea-sured and predicted results confirm the validity of the tire model.

The results of experimental determination of the deflection andtire contact area over a rigid surface, on function of inflation pres-sure and tire load presented here, show behavior and similar ten-dency to those obtained by other authors for agricultural tires withradial or diagonal plies (Kumar and Dewangan, 2004; Sharma andPandey, 1996; Upadhyaya and Wulfsohn, 1990; Wulfsohn and Up-adhyaya, 1992), supporting the selection of the 3.5 � 10 tire forrepresent the behavior of the agricultural tire.

2.3. Development of the finite element model of the soil compaction

Finite element model of tire–soil interaction represented thesoil compaction process caused by the traffic of a 3.5 � 10 tire withtwo load levels and different inflation pressures on a homogeneouslayer of a Rhodic Ferralsol soil. The effects of tire traffic over soilwere obtained from the interaction of the tire and soil models.

The soil represented in the model is a portion of the soil binwhere the experiments were carried out. To improve the computa-tional efficiency, the geometric domain was calibrated by makingsimulations varying the dimensions of the soil block representedin the model, in the three main axes. Then the smallest dimensionswere selected where borders conditions do not influence on the re-sults of a control variable (vertical stress). Later on, this require-ment was verified by means of three simulations in which keptconstant all the component elements of the model and three bor-ders conditions were varied. A correlation analysis was applied todetermine the correlation between the three curves of verticalstress to different soil depths for the three different borders condi-tions, being obtained a high statistical significance of the correla-tions, higher to 0.99 in the three cases. This procedure allowedthe selection of the smallest dimensions of the soil block in whichthe border conditions did not exert influence in the predictions re-sults, thus the computational efficiency was improved. The se-lected dimensions were: 0.7 m (Z axis), 0.4 m (X axis) and adepth of 0.4 m (Y axis).

González (2011) and Herrera (2006) determined that experi-mental results of the stress–strain curves of Rhodic Ferralsol soilfit with the Drucker Prager Extended constitutive model. It hasbeen used for modeling the elasto-plastic behavior of granularmaterials such as agricultural soils, where the material becomesstronger, as the pressure increases, allowing a material to hardenand/or soften isotropically. It generally allows for volume changeswith inelastic behavior; the flow rule, defining the inelastic strain-ing allows simultaneous inelastic dilation (volume increase) and

150 O. González Cueto et al. / Computers and Electronics in Agriculture 99 (2013) 146–152

inelastic shearing (Abaqus, 2008). Drucker Prager material modelhas been used in tire–soil interaction modeling (Biris et al., 2009;González, 2011).

Formulations of constitutive models, in terms of total stressinstead of effective stress have been based and used by differentauthors (González, 2011; Herrera, 2006; Hettiaratchi and O’Calla-ghan, 1980; Kirby et al., 1997; Kirby and Zoz, 1997; Poodt et al.,2003; Wulfsohn et al., 1998). These are simpler and convenientfor a very complex loading conditions caused by the tires andtracks in agriculture.

Soil moisture is the variable that has the greatest influence onthe compaction process (Hamza and Anderson, 2005). Thisdetermines the maximum value achievable of bulk density. Foreach soil type and compactive effort there is a particular value ofwater content, known as the optimum water content at which amaximum value of bulk density is obtained (Craig, 2007). Opti-mum water content for compaction in this soil is 31 g 100 g�1

(González, 2011). From this value the soil water contents for sim-ulation of soil compaction were selected. Two different soil watercontents, 25 and 30 g 100 g�1 of gravimetric water content wereestablished. The first moisture is 0.8wopt – a soil water contentwhere it is expected low soil compaction due to soil tends to bestiff and difficult to compact – and the last moisture is 0.96wopt –a soil water content where it is expected high soil compaction pro-voked by traffic.

Triaxial and direct shear tests were used to determine constitu-tive parameters of the soil. Poisson’s coefficient was calculated likeG = E/2(1 + m) (Wulfsohn and Adams, 2002), and the Young’s mod-ulus of elasticity was determined as the tangent module of theelastic strain section of the soil stress–strain curve. The friction an-gle of the material (b) was obtained as the slope of the linear yieldsurface in the p–t stress plane (Abaqus, 2008). Dilatancy angle (w)is zero in the clays or silts not consolidated. However, it has astrong influence on the overconsolidated soils or sands (PLAXIS,2004). In the soil with 25 and 30 g 100 g�1 of water contentw = 0, but in order to assess the original Drucker–Prager model thatestablish w = b, an associative flow rule setting w = b and K = 1 wasestablished in the first soil condition. Table 1 shows the constitu-tive parameters used in the simulations.

The agricultural operations are carried out to low speed. As a re-sult, a quasi-static modeling of soil–tool interaction is suitable(Rosa and Wulfsohn, 1999; Shoop, 2001). In this way, the dynamiceffects are avoided. The model was implemented in three steps. In

Fig. 6. Tire–soil interaction model discretized.

the first step, inflation pressure was applied to tire, in the secondone, the tire load was applied, and in the last one, a tangentialvelocity of 1 m s�1 was applied to tire. The contact between tireand the soil block was implemented as it was described in Sec-tion 2.1. Regarding the block soil discretization, it was made with8-node linear brick elements with reduced integration (C3D8R).

The mesh density was determined with a convergence analysis,which is similar to the one described in Section 2.1. The mesh wasmore refined at the neighborhood of the tire–soil contact area. Therange of the element size was between 0.01 and 0.025 m, On theother hand, in places away from tire–soil contact area, the meshdensity decreases. In this way, the computational efficiency wasimproved (Fig. 6).

2.4. Validation of the finite element model of the soil compaction

The validation of the finite element model of the soil compac-tion was carried out at the soil bin in the Centro de MecanizaciónAgropecuaria of the Universidad Agraria de la Habana, Cuba. A sin-gle tire testing machine was used. The soil bin which was used forthese tests was 8.0 m long, 1 m wide and 0.6 m deep. This soil binwas developed for testing agricultural implements and tires. Thesoil used in the traffic experiments was a Rhodic Ferralsol (clay loa-my). It was taken from an agricultural area located in San José delas Lajas, Mayabeque province in Cuba. Its coordinates are23�00006.270 0 north latitude and 82�08035.390 0 west longitude. Thesamples were obtained from five trenches made along the diago-nals of the field. From this soil samples were taken for the determi-nation of its properties (Table 2) and the other part was sieved anddeposited at the soil bin.

The soil bin was divided into two areas of 4 m long. The first onewas used for the initial displacement and tire stabilization and thesecond was for the measurements. Five load cells were placed in-side the soil bin. They were separated a long of 0.3 m each otherinside the soil bin, in the center of the tire print. Three load cellswere placed to 0.10 m of depth and two to 0.25 m of depth. The soilbin was filled and later compacted, obtaining a homogeneous layerof 1.0 Mg m�3 of bulk density. To establish the soil moisture con-tents, two weeks before the experiment the soil bin was irrigatedand it was left in rest so that it dried off and it reached the watercontent of 25 or 30 g 100 g�1.

Four experiments were carried out for each water contents andthe vertical stress on the load cells was evaluated. The tire was dri-ven at 1.0 m s�1.

Table 3 shows the inflation pressure and tire loads applied inthe experiments. The first traffic test of each soil water contentwas developed after the soil bin was prepared. The following testswere run on the print of the previous race.

Fig. 7 shows the field output of vertical stress for simulation ofthe experiment number III and Figs. 8 and 9 show the experimentaland predicted vertical stresses for each soil water contents. Thesefigures show how the tire inflation pressure, contact stress and tireload influence on the vertical stresses transmitted to soil profile.Simulated and observed stresses after wheel traffic agree well.The model predicted the trend and behavior of the stresses trans-missions in the soil. The calculated vertical stresses were underes-timated by 15% and 20% with respect to the measurements of theload cell at depths of 0.10 and 0.25 m, respectively. These differ-ences can be explained due to the remolded structure of the soil;a common problem in soil bin studies (Rosa and Wulfsohn, 1999).

The relationship between the tire inflation pressure, contactstress and tire load with soil compaction can be seen in Fig. 8.The runs I and II show the tire behavior when it is inflated witha pressure of 100 and 325 kPa under a load of 0.7 kN. In theseconditions, the tire causes contact stresses of 100 and 240 kPa,respectively. The highest vertical stresses were obtained in run II

Table 2Properties of the Rhodic Ferralsol soil used in the experiment.

Gs, (g cm�3) Consistency limits (%) Particle size (%) OM (g 100 g�1)

LL PL PI Sand Silt Clay

2.67 65.6 30.0 35.6 18.33 40.67 41 2.86

Where, Gs – specific gravity; LL – liquid limit; PL – plastic limit; PI – plastic index; OM – organic matter.

Table 3Inflation pressures and tire loads for each test.

Water content 25 (g 100 g�1) Water content 30 (g 100 g�1)

Experimentnumber

Pi(kPa)

L(kN)

Experimentnumber

Pi(kPa)

L(kN)

I 100 0.7 V 100 0.7II 325 0.7 VI 325 0.7III 325 2.3 VII 325 2.3IV 100 2.3 VIII 100 2.3

Where, Pi – tire inflation pressure; L – tire load.

00 50 100 150 200 250

Vertical stress (kPa), W = 30% Run V

Exp V

0.05

0.1

0.15

0.2

0.25

Dep

th, m

Run VI

Exp VI

Run VII

Exp VII

.

0.3

0.35

Run VIII

Exp VIII

Fig. 9. Experimental and predicted vertical stresses for soil with 30 g 100 g�1 ofwater content.

O. González Cueto et al. / Computers and Electronics in Agriculture 99 (2013) 146–152 151

on contact area. The difference in vertical stresses transmitted tothe soil was bigger in the top layer and negligible after a depthof 0.08 m. In this case the inflation pressure and tire contact stres-ses influence only on the superficial layer and to a depth of 0.08 m.Runs III and IV show a similar behavior for a tire loaded with2.3 kN. In this case the influence of inflation pressure and contactstress reaches a depth of 0.14 m, due to the effect of a bigger load.The effect of the tire load on the propagation of the vertical stressesalong the depth is shown when the runs I–IV, and II–III are com-pared. Both couples possess the same Pi and contact stress. Theincrement of the tire load causes the increase of the soil vertical

Fig. 7. Field output of vertical stress for simulation of the experiment number III.

00 50 100 150 200 250

Vertical stress (kPa), W = 25% Run I

Exp I

0.05

0.1

0.15

0.2

0.25

Dep

th, m

Run II

Exp II

Run III

Exp III

0.3

0.35

Run IV

Exp IV

Fig. 8. Experimental and predicted vertical stresses for soil with 25 g 100 g�1 owater content.

f

stress, becoming bigger the difference in the layer between 0 and0.15 m. This increment reaches almost 100%. These results showthat contact stress and tire inflation pressure influence the verticalstresses only at the top layer, where most of the soil compactiontakes place. Below 0.15 m of depth, only the tire load generatesvertical stresses. The tire load determines the rate at which the ver-tical stress decreases along the depth. Based on the equation rz =p(1 � cosca), (Söhne, 1953, 1958), where: rz – the vertical stress;p – mean normal stress acting in the contact area; c – the concen-tration factor and a – the half aperture angle between the point atdepth z and the contact area’s edge; Alakukku et al. (2003) referthat tire load determines the variation of the vertical stress levelin the soil profile as the depth is increased. However, such stresseswill never exceed the peak contact stress. Several authors haveoutlined that superficial layer compaction depends on the contactstress, tire inflation pressure and tire load and the subsoil compac-tion depends only on the tire load (Alakukku et al., 2003; Hamzaand Anderson, 2005). These results are in line with the predictionspresented in this paper.

The physical properties of the soil remain constant if the exter-nal load does not exceed its internal strength, which is determinedby the yield stress or precompression stress. Otherwise, the soilphysical properties change due to the plastic deformation (Lebertand Horn, 1991). Only stresses above the yield stress cause plasticand irreversible deformation. Fig. 9 shows the vertical stress trans-mission with the depth, for the soil with 30 g 100 g�1 of water con-tent. It maintained a trend and similar behavior to the soil with25 g 100 g�1 of water content (Fig. 8). Although the values of thevertical stresses of the soil are similar, the compaction of the wetsoil should be higher to the dry soil. In a wet soil, the yield stressis smaller (Table 1, Section 2.3). Thus, irreversible deformationsand soil compaction will be caused with smaller vertical stresses.In the soil with 25 g 100 g�1, the yield stress is 106 kPa, and greatervertical stresses were obtained only in the top layer (Fig. 8), whichare in the range of depth between 0 and 0.08 m; therefore, this it isthe area where soil compaction should be expected. Alternatively,the yield stress is 55 kPa in the soil with 30 g 100 g�1 of water con-tent. Greater vertical stresses were obtained only (Fig. 9) in the soilwith 0–0.14 m depth. The soil compaction extended to a deeperdepth. In both soil conditions, the compaction takes place only inthe superficial layer, reaching a maximum depth of 0.14 m. The soil

152 O. González Cueto et al. / Computers and Electronics in Agriculture 99 (2013) 146–152

strength decreases with the increase of water content; therefore,the tire induced a bigger soil deformation at the contact and adja-cent areas in soil with more water content.

3. Conclusion

It was developed a three-dimensional finite element model ofsoil compaction caused by agricultural tire traffic which was vali-dated in experiments on a soil bin. The model predicts the effectof inflation pressures, ground pressure and tire load on the stresseson the contact and the soil profile, it can be used in both teachingand research. The model was used to predict the depth at whichsoil compaction was produced for each combination of tire infla-tion pressure and tire load, and the relationship between the tireinflation pressure, contact stress and tire load with soil compac-tion. The model showed that magnitudes of vertical stresses trans-mitted to soil are independent to water content and that more soilcompaction in wet soils depends on the less yield stresses in thoseconditions. Besides, the good agreement of the model with exper-imental results demonstrates the validity of using the ExtendedDrucker Prager model to represent the mechanical response ofthe Rhodic Ferralsol soil.

Acknowledgments

This research was funded by a research grant of the Science,Technology and Environment Ministry of Cuba in Villa Clara prov-ince. The study was also supported by Centro de Investigación enMétodos Computacionales y Numéricos en la Ingeniería de la Uni-versidad Central ‘‘Marta Abreu’’ de las Villas.

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